A real-time thermal field theoretical analysis of Kubo-type shear viscosity : Numerical understanding with simple examples

A real-time thermal field theoretical calculation of shear viscosity has been described in the Kubo formalism for bosonic and fermionic medium. The two point function of viscous stress tensor in the lowest order provides one-loop skeleton diagram of boson or fermion field for bosonic or fermionic matter. According to the traditional diagrammatic technique of transport coefficients, the finite thermal width of boson or fermion is introduced in their internal lines during the evaluation of boson-boson or fermion-fermion loop diagram. These thermal widths of $\phi$ boson and $\psi$ fermion are respectively obtained from the imaginary part of self-energy for $\phi\Phi$ and $\psi\Phi$ loops, where interactions of higher mass $\Phi$ boson with $\phi$ and $\psi$ are governed by the simple $\phi\phi\Phi$ and {\ov\psi}\psi\Phi interaction Lagrangian densities. A two-loop diagram, having same power of coupling constant as in the one-loop diagram, is deduced and its contribution appears much lower than the one-loop values of shear viscosity. Therefore the one-loop results of Kubo-type shear viscosity may be considered as leading order results for this simple $\phi\phi\Phi$ and {\ov\psi}\psi\Phi interactions. This approximation is valid for any values of coupling constant and at the temperatures greater than the mass of constituent particles of the medium

A comparative analysis of in-medium spectral functions for N(940)N(940) and N∗(1535)N^*(1535) in real-time thermal field theory

In the real-time thermal field theory, the nucleon self-energy at finite temperature and density is evaluated where an extensive set of pion-baryon ($\pi B$) loops are considered. On the other side the in-medium self-energy of $N^*(1535)$ for $\pi N$ and $\eta N$ loops is also determined in the same framework. The detail branch cut structures for these different $\pi B$ loops for nucleon $N(940)$ and $\pi N$, $\eta N$ loops for $N^*(1535)$ are addressed. Using the total self-energy of $N(940)$ and $N^*(1535)$, which contain the contributions of their corresponding loop diagrams, the complete structures of their in-medium spectral functions have been obtained. The Landau and unitary cut contributions provide two separate peak structures in the nucleon spectral function while $N^*(1535)$ has single peak structure in its unitary cuts. At high temperature, the peak structures of both at their individual poles are attenuated while at high density Landau peak structure of nucleon is completely suppressed and its unitary peak structure is tending to be shifted towards the melted peak of $N^*(1535)$. The non-trivial modifications of these chiral partners may indicate some association of chiral symmetry restoration

Low mass enhanced probability of pion in hadronic matter due to its Landau cut contributions

In the real-time thermal field theory, the pion self-energy at finite temperature and density is evaluated where the different mesonic and baryonic loops are considered. The interactions of pion with the other mesons and baryons in the medium are governed by the effective hadronic Lagrangian densities whose effective strength of coupling constants have been determined from the experimental decay widths of the mesons and baryons. The detail branch cut structures of these different mesonic and baryonic loops are analyzed. The Landau cut contributions of different baryon and meson loops become only relevant around the pion pole and it is completely appeared in presence of medium. The in-medium spectral function of pion has been plotted for different values of temperature, baryon chemical potential as well as three momentum of the pion. A noticeable low mass probability in pion spectral function promise to contribute in the low mass dilepton enhancement via indirect modification of $\rho$ self-energy for $\pi\pi$ loop

The nucleon thermal width due to pion-baryon loops and its contribution in Shear viscosity

In the real-time thermal field theory, the standard expression of shear viscosity for the nucleonic constituents is derived from the two point function of nucleonic viscous stress tensors at finite temperature and density. The finite thermal width or Landau damping is traditionally included in the nucleon propagators. This thermal width is calculated from the in-medium self-energy of nucleon for different possible pion-baryon loops. The dynamical part of nucleon-pion-baryon interactions are taken care by the effective Lagrangian densities of standard hadronic model. The shear viscosity to entropy density ratio of nucleonic component decreases with the temperature and increases with the nucleon chemical potential. However, adding the contribution of pionic component, total viscosity to entropy density ratio also reduces with the nucleon chemical potential when the mixing effect between pion and nucleon components in the mixed gas is considered. Within the hadronic domain, viscosity to entropy density ratio of the nuclear matter is gradually reducing as temperature and nucleon chemical potential are growing up and therefore the nuclear matter is approaching toward the (nearly) perfect fluid nature

Analysis of ω\omega self-energy at finite temperature and density in the real-time formalism

Using the real time formalism of field theory at finite temperature and density we have evaluated the in-medium $\omega$ self-energy from baryon and meson loops. We have analyzed in detail the discontinuities across the branch cuts of the self-energy function and obtained the imaginary part from the non-vanishing contributions in the cut regions. An extensive set of resonances have been considered in the baryon loops. Adding the meson loop contribution we obtain the full modified spectral function of $\omega$ in a thermal gas of mesons, baryons and anti-baryons in equilibrium for several values of temperature and baryon chemical potential